Let A = 1 2 3 4 1 - 1 2 , then the value of sum of all the elements of A 100 is

Question: Answered & Verified by Expert

Let

A = [\begin{matrix} \frac{1}{2} & \frac{3}{4} \\ 1 & \frac{- 1}{2} \end{matrix}]

, then the value of sum of all the elements of

A^{100}

MathematicsMatricesJEE Main

Solution:

1775 Upvotes Verified Answer

The correct answer is: 2

A^{2} = [\begin{matrix} \frac{1}{2} & \frac{3}{4} \\ 1 & \frac{- 1}{2} \end{matrix}] [\begin{matrix} \frac{1}{2} & \frac{3}{4} \\ 1 & \frac{- 1}{2} \end{matrix}] = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]

\Rightarrow A^{2} = Ι \Rightarrow A^{100} = Ι \Rightarrow s u m = 2

Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.